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The ergodic capacity in Rayleigh fading of multi-hop wireless transmission systems employing either amplify-and-forward relaying or decode-and-forward relaying is studied, assuming channel state information is only known at the receiving terminals. Two upper bounds based on Jensen's inequality and the harmonic-geometric means inequality as well as an infinite series representation for the ergodic capacity of an amplify-and-forward multi-hop transmission system is derived. Numerical results indicate the upper bound obtained based on Jensen's inequality is tight. This upper bound is tighter than the upper bound based on harmonic and geometric means for larger numbers of hops and especially for systems in non-identical fading.
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